Effective Mathematics Teaching Practice 4: Facilitate Meaningful Mathematical Discourse

Instructional Support Menu

NCTM’s effective mathematics teaching practice facilitate meaningful mathematical discourse has come to be seen as somewhat of a “meta-practice” that includes several others, such as pose purposeful questions, use and connect mathematical representations, and elicit and use evidence of student thinking. All of these practices come together to shape the way thinking is supported and communicated in a mathematics classroom.

The most widely used guide for facilitating discourse in mathematics classrooms is 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein. (Yes, this gets a bit confusing, as this one NCTM effective teaching practice leans heavily on the work of a book called 5 Practices, which maybe is better thought of as an instructional model for teaching a lesson.) The five practices are (pp 9-10):

1. Anticipating likely student responses to challenging mathematical tasks and questions to ask to students to produce them;
2. Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups);
3. Selecting particular students to present their mathematical work during the whole-class discussion;
4. Sequencing the student responses that will be displayed in a specific order; and
5. Connecting different students’ responses and connecting the responses to key mathematical ideas.

Whether or not a teacher is following the 5 Practices instructional model or not, the goal is to shift teaching away from the teacher being the dominant speaker and information authority and to build a shared culture where students lead conversations themselves and the teacher is there to probe into thinking more deeply, connect students' ideas, and sharpen the students' collective understanding.

• View All 8 Effective Mathematics Teaching Practices

One of the ways NCTM (2014, p. 35) summarizes the practice of facilitate meaningful mathematical discourse is by describing a set of actions expected of teachers and students that indicate engagement in this teaching practice.